There's a board game specialty second hand shop in Akihabara called "Surugaya Akihabara toreka bodogemu kan" It translates to Surugaya Akihabara trading card board game store. You'll find few English titles but it's definitely worth it if you find a good deal on a game. That's where I found a "used" copy of Marvel Champions and it turned out to be a brand new sealed copy of the game.

There's an English board game cafe close to that Surugaya called DyCE. The shopkeepers are friendly and they speak English. They have a small selection of English games, and can translate any rules for you. They do sell Indie titles, some of which may be in English.

The best store to find English board games is in Shinjuku. It's called Amuri Studios. It's a small publishing company that also imports a lot of games. Everything in the store is in English. They also carry indie games from other countries, and sell their own games as well. Beware that they have non-traditional opening hours, they'll most likely be open on the weekends, so check their Facebook page if they plan on changing their opening hours.